Bound States at Threshold resulting from Coulomb Repulsion

TL;DR

This paper proves that in non-relativistic quantum systems with Coulomb interactions, bound states approaching the dissociation threshold remain localized and become true bound states at threshold, with applications to atomic ionization.

Contribution

It establishes conditions under which bound states at the Coulomb threshold do not spread and become genuine bound states, extending understanding of atomic and nuclear systems.

Findings

Bound states at Coulomb thresholds do not spread and become true bound states.

Atomic ion with critical charge in (N_e -2, N_e -1) has a bound state at threshold.

Results apply to systems with fermionic electrons and finite nuclear mass.

Abstract

The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction on the particle statistics is imposed. It is proved that if the lowest dissociation threshold corresponds to the decay into two likewise non-zero charged clusters then the bound state, which approaches the threshold, does not spread and eventually becomes the bound state at threshold. The obtained results have applications in atomic and nuclear physics. In particular, we prove that atomic ion with atomic critical charge $Z_{cr}$ and $N_e$ electrons has a bound state at threshold given that $Z_{cr} \in (N_e -2, N_e -1)$, whereby the electrons are treated as fermions and the mass of the nucleus is finite.